5

1 1 | 42 1...

Question

1 1 | 42 1

1 1 | 42 1



Answers

$\left[ \begin{array}{lll}{1} & {1} & {1} \\ {1} & {2} & {3} \\ {0} & {1} & {1}\end{array}\right]$

In this video, we're gonna go through the answer. Question number three from chapter 9.5 for us to find the inspectors American values off this matrix A So let's find values for me to look at the seven off a minus. Ah, I That's a deterrent. Off the matrix one minus ah. Minus 1 to 4. Minus R. So that is one minus. Uh, which the top left and component times by top. Right and bottom right hand component, which is four minutes out. Minus two minus one plus two. Okay, yes, this is gonna be equal. Thio Ah. Squared. Uh, minus are his forearms minus five plus four plus two is plus six. We have fact arise that it's gonna be ah, minus two. Um, on this three. And if we set that equal to zero, then the solutions are are equal to two. And I was it was a three, which are too like values for 6 a.m. On the vectors come calculated by first finding the matrix. Hey, minus first Eigen. But value times I times by in fact, if you want, But she's gonna be our vector equal to zero. So a minus two I s That's gonna be one minus two is minus one months. Want to four Minus two is too size by you. Want is equal to zero. I guess that means that that I convict you won must have the bomb component as minds one times the top components and some bone is one bomb component is minds. Well, that's our first. Like a better second wagon back dirt is calculated by the matrix a minus. The second I value times I tell you to equal Sarah. So a minus three i b minus two minus one, 24 Ministry is one times you say equal Sarah. So that implies that you too. If the first component is one, then lower component needs to bay minus two times the top opponent, which is just minus two. There are two. You come back this way

Okay for this one. We have a is equal to 12 negative. One 011 and zero. Negative 11 So the characteristic equation for this problem is given by negative Lambda Cubed plus three Lambda squared minus four. Lambda plus two is equal to zero. And when we solve this equation, it's a cubic equation. So you will get the three argon values as 11 plus I and one minus. I noticed that these talking visor complex congregants. So now if we have the Lambda equals one, then upon solving the system, eh? Minus I times u equals zero. We will get that use equal t times 100 and for Lambda equals one. Plus I, using a similar process, we end up getting that you sequel to a T times I'm minus two negative I and one no, for Lambda Contra Kit equals one minus I, which is given here. Then that implies that you is equal to it. Turns out that the Egan vectors are also conflicts congregates of each other. So you was simply gonna be equal to a T times negative. I'm minus two guy and one

We want to use a calculator to find the inverse of a matrix. I'm going to illustrate this with the decimals matrix calculator. So we're going to hit new matrix, identify this as a three by three matrix and then put in the elements 120 which is optional, type -1, -1 2 -10. Want us to find, then you just type Matrix A. And then the inverse. And you can then identify the inverse as 0.20 point 4.40 negative point to 1.4 negative one negative 1.2. Yeah.

In this video to go through the answers. Question number nine from chapter 9.3 through us to find the inverse off the matrix two minus one minus one before. So we want to construct the combination. Thanks. Matrix. With the identity, that's just 1001 Then we convert reduce this. Okay, so we want to add half of top line to the bottom line. Seven top line stays the same. And the bottom line this is gonna go to zero than four. Minus 1/2 is just gonna be, you know, half with seven over too. Oh, one is 1/2 and this one stays the same the next time we can, at times the bottom row by at times, the bottom row by two over seven. That's right. That second component equal to one that's a topper stays the same. 012 over seven. This is gonna be a one of the seven to over seven. Next time we can add one of the bottom roads, the toppers. So that's just 10 that's already asked me to. At 20 is two months. One plus one is zero. One plus. Seventh is 8/7 to you plus size zero plus +276 to 7. Bomber saysthe. Same 01 1/7 2 7th Okay, There's no need to do to get the left outside. Equally identity is more supply. The top row by half. That gives us 10 for seventh on 1/7. Bummer is the same as it goes before 01 17 to seventh. So then this matrix is the inverse off the major crew given They were asked to check that using the formula, which is question number three. That's right. Formula number three from the textbook. So we want to find the inverse off this. That's that's gonna be one over. It was a d minus. BC If it is not zero So two times for AIDS minus minds one thought months won't you won't. And then we just gotta swap them around. The top left becomes the bomb. Well, the bottom right was which is four minus b might see on dde A, which is to So is this just gonna be won over? Step one of the eight minus one is the seventh. So it's gonna be 47 17 17 two sevens, which is equal to the for Oh, the inverse


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